Einstein's postulates and the Michelson-Morley experiment: VCE Physics Unit 4

What this dot point is asking

The VCAA Physics Study Design (Unit 4, Area of Study 1) asks you to describe where classical mechanics breaks down for very fast motion, state the two postulates of Einstein's special theory of relativity, interpret the null result of the Michelson-Morley experiment, and compare special relativity with classical principles. This page covers those four ideas. The equations come on the next pages.

Classical mechanics and its limit

In classical (Newtonian) mechanics, time passes at the same rate for everyone and lengths do not depend on who measures them. Velocities simply add. If a train moves at $20$ m s$^{-1}$ and a passenger walks forward at $2$ m s$^{-1}$ relative to the train, someone on the platform measures $22$ m s$^{-1}$. This works extremely well for everyday speeds.

Near the speed of light it fails. Measurements of fast-moving particles show that their kinetic energy and momentum do not follow the classical formulas, and that nothing with mass can be accelerated to $c$. The classical picture is not wrong so much as a very good approximation at speeds much smaller than $c$. Special relativity includes it as the low-speed limit.

Inertial frames of reference

A frame of reference is the viewpoint from which an observer measures positions, times and speeds. An inertial frame is one that is not accelerating: it is at rest or moves in a straight line at constant speed. A lab bench is close to inertial for short experiments. A car braking hard or going around a bend is not.

Special relativity deals only with inertial frames. Two observers in different inertial frames each have an equally valid view of the same events.

Einstein's two postulates

A postulate is a starting assumption that is not derived from anything simpler. It is different from a theory, which is a whole framework built on postulates and then tested. Einstein published the theory in 1905 and built it on two postulates.

1. Physical laws take the same form in every inertial frame of reference. No experiment done inside a smoothly moving laboratory can tell you that you are moving, or how fast. There is no special "at rest" frame.
2. The speed of light in a vacuum has the same value, $c$, whichever inertial observer measures it and whether or not the source is moving.

The second postulate is the surprising one. If you chase a light beam at $0.9c$, you still measure its speed as $c$, not $0.1c$. If a torch is thrown towards you at $0.9c$, the light still arrives at $c$, not $1.9c$. Classical velocity addition cannot describe this, so something in classical thinking has to give. What gives is the idea that time and length are the same for all observers.

Comparing special relativity with classical physics

Both agree when $v \ll c$. Relativity only shows its effects when $v$ is a significant fraction of $c$.

The Michelson-Morley experiment

Before Einstein, physicists believed light, as a wave, needed a medium to travel through. They called it the luminiferous aether, imagined as filling space. If the aether existed, Earth would be moving through it as it orbits the Sun, producing an "aether wind", and the speed of light measured on Earth would depend on direction: faster with the wind, slower against it.

In 1887, Albert Michelson and Edward Morley used an interferometer to look for this. A beam of light was split into two beams that travelled along perpendicular arms, were reflected back and recombined. If light moved at different speeds along the two arms because of an aether wind, the beams would arrive out of step and the interference fringes would shift when the apparatus was rotated.

They saw no significant shift. This is the null result: no detectable difference in the speed of light with direction, and so no evidence of motion through an aether.

Interpretation. The null result is exactly what the second postulate predicts. Light has the same speed in every direction and for every inertial observer, because there is no aether frame to measure it against. The experiment did not prove special relativity, but it is strong evidence consistent with it, and it removed the main reason for believing in an aether.

Worked example: light from a moving source

Try this

Q1. State Einstein's two postulates. [2 marks]

• Cue. Physical laws take the same form in every inertial frame; every inertial observer measures the same vacuum speed of light, whatever the source is doing.

Q2. Describe what the Michelson-Morley experiment was designed to detect and state what it found. [3 marks]

• Cue. It looked for a difference in the speed of light along perpendicular directions caused by Earth's motion through the aether, using interference fringes. No significant fringe shift was seen (a null result).

Q3. A torch on a spaceship moving at $0.50c$ away from you shines light towards you. What speed do you measure for the light? Justify your answer. [2 marks]

• Cue. $c$. By the second postulate the speed of light is independent of the motion of the source.